Reactance and frequency

Chapter Reactance and frequency

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • At high ac frequencies, the current through the coil will have difficulty followingthe voltage placed across the coil. Just as the coil starts to “think” that it’s making agood short circuit, the ac voltage wave will pass its peak, go back to zero, and then tryto pull the electrons the other way.This sluggishness in a coil for ac is, in effect, similar to dc resistance. As the fre-quency is raised higher and higher, the effect gets more and more pronounced. Even-tually, if you keep on increasing the frequency of the ac source, the coil will not evenbegin to come near establishing a current with each cycle. It will act like a large resis-tance. Hardly any ac current will flow through it.The opposition that the coil offers to ac is called inductive reactance. It, like re-sistance, is measured in ohms. It can vary just as resistance does, from near zero (ashort piece of wire) to a few ohms (a small coil) to kilohms or megohms (bigger and big-ger coils).Like resistance, inductive reactance affects the current in an ac circuit. But, unlikesimple resistance, reactance changes with frequency. And the effect is not just a de-crease in the current, although in practice this will occur. It is a change in the way thecurrent flows with respect to the voltage.Reactance and frequencyInductive reactance is one of two kinds of reactance; the other, called capacitive reac-tance, will be discussed in the next chapter. Reactance in general is symbolized by thecapital letter X. Inductive reactance is indicated by the letter X with a subscript L: XL.If the frequency of an ac source is given, in hertz, as f, and the inductance of a coilin henrys is L, then the inductive reactance isXL6 .28fLThis same formula applies if the frequency, f, is in kilohertz and the inductance, L,is in millihenrys. And it also applies if f is in megahertz and L is in microhenrys. Just re-member that if frequency is in thousands, inductance must be in thousandths, and iffrequency is in millions, inductance must be in millionths.Inductive reactance increases linearly with increasing ac frequency. This meansthat the function of XL vs f is a straight line when graphed.Inductive reactance also increases linearly with inductance. Therefore, the func-tion of XL vs L also appears as a straight line on a graph.The value of XL is directly proportional to f; XL is also directly proportional to L.These relationships are graphed, in relative form, in Fig. 13-4.Problem 13-1Suppose a coil has an inductance of 0. 50 H, and the frequency of the ac passing throughit is 60 Hz. What is the inductive reactance?Using the above formula, XL6.28600. 50 188.4 ohms. You should round thisoff to two significant digits, or 190 ohms, because the inductance and frequency areboth expressed to only two significant digits.Reactance and frequency233